Dr. Brewster on the laws of polarisation, 245 
Sect. IV. On the resolution and combination of polarising forces, 
and the reduction of all crystals to crystals with two or more 
axes. 
It has been remarked by M. Biot in one of his latest me- 
moirs, that it has been established by Laplace, that if the 
Huygenian law is admitted, the extraordinary refraction is 
necessarily produced by a repulsive force; and the same 
philosopher has also asserted, that from the opposite character 
of the tints produced by beryl and quartz, there results ne- 
cessarily this alternative : “ Either the forces which produce 
the extraordinary refraction are repulsive in one of the 
classes and attractive in the other, or they are repulsive in 
both ; but they turn the axes of the luminous molecules in 
directions inversely rectangular. New experiments have 
proved to me that the first mode is that which nature 
realises.” * 
This view of the subject of double refraction and polari- 
sation has always appeared to me erroneous. I have never 
been able to perceive that the phenomena of calcareous spar 
were necessarily referable to a repulsive force, or that nature 
had restricted herself to any of the alternatives which have just 
been stated. These opinions have acquired new strength as I 
advanced in the inquiry, and I trust I shall be able to demon- 
strate, not only that the phenomena of double refraction and 
polarisation may be explained by forces or combinations of 
forces different from those which have been given by Laplace 
and Biot, but that there are certain analogies of nature, 
and certain physical circumstances in the phenomena, which 
• Mem . de l ’ Institut . Lu, 2 Jan. 1815. 
